In order to apply optimization algorithms to design optimization problems it is essential to find ways to describe the shape of a design by a set of parameters which can be modified by the optimization algorithm. A well known method is for example to define a spline line for two dimensional surfaces or a spline surface for three dimensional designs, which describe the surface of the object which is to be optimized. In this case the parameters which are modified by the optimization algorithms are the control and knot points, and in the case of NURBS (non rational B-splines) additionally the weights of the control points. Another way of representing a given design is to define a transformation function which transforms the space in which a basic design is given. In this case a variation of a shape can be realized by modifying parameter of a transformation function. These methods can be summarized under the term of free form deformation.